- 1 Avis, D. On the complexity of finding the convex hull of a set of points. Tech. Rep. SOCS 79.2, McGdl Umverslty, Montreal, Ontano, Canada, 1979Google Scholar
- 2 GRAHAM, R L An efficient algorithm for determining the convex hull of a t'mite set. Inf. Proc. Lea. 1 (1972), 132-133.Google Scholar
- 3 SHAMOS, M.I. Computational geometry. Tech. Pep., Computer Science Dep., Carnegie-Mellon Umv., Pmsburgh, Pa, May 1978.Google Scholar
- 4 VAN EMDE BOAS, P. On the f~(n log n) lower bound for convex hull and maxtmal vector determination. Inf. Proc. Left. 10 (1980), 132-136.Google Scholar
- 5 YAO, A C A lower bound to finding convex hulls. Tech Rep. STAN-CS-79-733, Computer Science Dep., Stanford, Univ., Stanford, Cahf., Apnl 1979. Google Scholar
Index Terms
- A Lower Bound to Finding Convex Hulls
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